Linear Motion Notes
Distance – scalar value describing the length of the path physically travelled
Displacement – vector value describing the change in position (straight line from start to
end) including direction
Speed – scalar – describing how fast something is moving
Velocity – vector – speed in a particular direction or change in displacement over a time
Acceleration – vector – change in velocity during over a time
 A zero acceleration indicates no change in velocity.
 A change in velocity can be either a change in speed or a change in direction
Direction is mostly noted by using a positive or negative. Positive displacement and
velocity are to the right and up, negative are to the left and down.
If velocity and acceleration are in the same direction (have the same sign) the object’s
velocity is increasing. If they are in opposite directions, the object’s velocity is
decreasing.
Motion Graphs
Position vs. Time graph (x vs t)
 The slope of a position vs. time graph describes the velocity.
 A steeper slope means a faster velocity; shallower slope is a slower velocity
 A positive slope indicates a positive velocity or movement in a positive
direction (and a negative slope indicates a negative velocity)
 A curve on a position graph indicates a change in the velocity or an
acceleration.
Velocity vs. Time graph (v vs t)
 The slope of a velocity vs. time graph describes the acceleration and follows
all the same trends as listed above. Steep slope = large acceleration. Positive
slope = positive acceleration
 The area underneath the line of a velocity graph describes the change in an
objects position, or its displacement.
Acceleration vs. Time graph (a vs t)
 The area under the line of an acceleration graph describes the change in
velocity of an object.
Free fall
 Acceleration of a free-fall object is always – 9.8 m/s2
 If an object is simply dropped from some height,
o its initial velocity is 0 m/s2
o its displacement is negative
 An object that is thrown up will return to the original position with an equal
but opposite (negative) velocity.
 At the top of an object’s path its velocity will be 0 m/s2
 It takes the same amount of time for an object to reach the top as it does to
come back to its starting position
Problem solving steps
1. Draw a picture 
2. List your variables and identify what you know
 t – time
 x – displacement
 v0 – initial velocity
 v1 – final velocity
 a – acceleration
3. Choose an equation
v
x
t
v  v0
2
v
a
t
v
4. Solve, include units in your answer.
v  v0  at
1
x  (v0  v)t
2
1
x  v0t  at 2
2
2
2
v  v0  2ax